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Components in the space of composition operators

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Abstract

We consider the topological space of all composition operators, acting on certain Hilbert spaces of holomorphic functions on the unit disc, in the uniform operator topology. A sufficient condition is given for the component of a composition operator to be a singleton. A necessary condition is given for one composition operator to lie in the component of another. In addition, we prove analogous results for the component of the image of a composition operator in the Calkin algebra. Finally, we obtain some related results on the essential norm of a linear combination of composition operators.

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Authors and Affiliations

  1. Department of Mathematics, University of Richmond, 23173, Richmond, VA

    Barbara D. MacCluer

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  1. Barbara D. MacCluer
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Research supported in part by the National Science Foundation.

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MacCluer, B.D. Components in the space of composition operators. Integr equ oper theory 12, 725–738 (1989). https://doi.org/10.1007/BF01194560

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  • DOI: https://doi.org/10.1007/BF01194560

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